Trh CP ri riziko "korelaceA,B" I A 0.22 0.3 0.15 Trh Rp SigmaP Rp/SigmaP B 0.31 0.32 I 0.261589242 0.234659406 1.114761376 II A 0.26 0.29 -0.06 II 0.295148765 0.211251174 1.397146151 B 0.34 0.33 III 0.224674321 0.183191507 1.226445067 III A 0.18 0.2 0.09 B 0.41 0.38 Požadujeme na každém trhu portfolio s E(Rp)=25% Trh I CovMatice 0.09 0.0144 Matice soustavy VPS 0.0144 0.1024 0.18 0.0288 1 0.22 0 VPS 0.0288 0.2048 1 0.31 0 0.18 0.0288 1 0 1 1 0 0 1 0.0288 0.2048 1 0 0.22 0.31 0 0 0.25 1 1 0 1 wi Inv.Matice wi Rp VarP SigmaP 3.056234719 -3.056234719 0.537897311 w_a 0.537897311 0 2.52323E-15 3.444444444 -11.11111111 0.666666667 0.25 0.057777778 0.240370085 1.040062868 -3.056234719 3.056234719 0.462102689 w_b 0.462102689 0 -2.52323E-15 -2.444444444 11.11111111 0.333333333 0.537897311 0.462102689 -0.110130073 -0.110130073 3.444444444 -2.444444444 -2.874320988 10.56691358 lambda1 -0.232592593 -11.11111111 11.11111111 10.56691358 -40.39506173 lambda2 0.468148148 Zkouska 1 Rp VarP SigmaP Zk: 0.261589242 0.055065037 0.234659406 Zk 1 1.00 0.00 0.00 0 2.52323E-15 3.444444444 -11.11111111 0.00 1.00 0.00 0 -2.52323E-15 -2.444444444 11.11111111 0.00 0.00 1.00 3.444444444 -2.444444444 -2.874320988 10.56691358 -11.11111111 11.11111111 10.56691358 -40.39506173 Trh II CovMatice 0.0841 -0.005742 -0.005742 0.1089 VPS 0.1682 -0.011484 1 0 -0.011484 0.2178 1 0 1 1 0 1 wi 2.445179085 -2.445179085 0.560640441 w_a 0.560640441 -2.445179085 2.445179085 0.439359559 w_b 0.439359559 0.560640441 0.439359559 -0.089254117 -0.089254117 Zkouska 1 Rp VarP SigmaP Zk: 0.295148765 0.044627059 0.211251174 1.00 0.00 0.00 0.00 1.00 0.00 0.00 0.00 1.00 Trh III CovMatice 0.04 0.00684 0.00684 0.1444 VPS 0.08 0.01368 1 0 0.01368 0.2888 1 0 1 1 0 1 wi 2.928772259 -2.928772259 0.805763824 w_a 0.805763824 -2.928772259 2.928772259 0.194236176 w_b 0.194236176 0.805763824 0.194236176 -0.067118257 -0.067118257 Zkouska 1 Rp VarP SigmaP Zk: 0.224674321 0.033559128 0.183191507 1.00 0.00 0.00 0.00 1.00 0.00 0.00 0.00 1.00 ##### Sheet/List 2 ##### Firma 1 Firma 2 Firma 3 Kovariance m 0.04 0.015 0.03 "s1,2" 2.3 s 0.6 0.04 0.055 "s1,3" -1.8 "s2,3" 0.3 Covar Matice 0.36 2.3 -1.8 2.3 0.0016 0.3 -1.8 0.3 0.003025 Matice soustavy vps 0.72 4.6 -3.6 1 0 4.6 0.0032 0.6 1 0 -3.6 0.6 0.00605 1 0 1 1 1 0 1 Rp VarP SigmaP Inver.M wi 0.022803245 0.150844806 0.388387443 0.058712622 0.01769581 0.113033983 -0.130729793 -0.003324559 -0.003324559 0.113033983 -0.117789523 0.00475554 0.477567281 0.477567281 -0.130729793 0.00475554 0.125974253 0.525757278 0.525757278 -0.003324559 0.477567281 0.525757278 -0.301689612 -0.301689612 zk 1 "Pozadovana vynosnost portfolia: 3,5%" Matice soustavy vps 0.72 4.6 -3.6 1 0.04 0 4.6 0.0032 0.6 1 0.015 0 -3.6 0.6 0.00605 1 0.03 0 1 1 1 0 0 1 0.04 0.015 0.03 0 0 0.025 Inv.M wi Rp VarP SigmaP 0.057018304 0.038012203 -0.095030506 -0.593808572 25.89473598 0.053559827 0.025 0.109699993 0.331209892 0.075480837 0.038012203 0.025341468 -0.063353671 1.604127618 -49.40350935 0.369039885 -0.095030506 -0.063353671 0.158384177 -0.010319046 23.50877337 0.577400288 -0.593808572 1.604127618 -0.010319046 8.565280306 -388.8468436 -1.155890784 25.89473598 -49.40350935 23.50877337 -388.8468436 17052.25902 37.45963193 1 ##### Sheet/List 3 ##### Emise CP1 CP2 CP3 CP4 CP5 CP6 CP7 ri (v %) CP1 80.5 82.7 85.3 85.1 123.9 22 3.5 1.9 CP2 82.7 184.7 131.5 69.4 49.5 58 -9.9 6.1 CP3 85.3 131.5 374.2 384.5 366.5 103.8 343.5 2.9 wi 2.137199771 0.04443472 -0.290668798 -0.230272848 -0.773325871 -1.12240341 1.235036437 CP4 85.1 69.4 384.5 684.8 599.1 51.6 502.7 4 CP5 123.9 49.5 366.5 599.1 871.4 -21.2 520.4 5.7 Vypocet VarP CP6 22 58 103.8 51.6 -21.2 89.7 74.4 3.4 367.6936402 7.85367765 -52.98983461 -41.8810356 -204.7759573 -52.77360681 9.238318563 CP7 3.5 -9.9 343.5 502.7 520.4 74.4 574.6 4.9 7.85367765 0.364679863 -1.698425925 -0.710108395 -1.700944652 -2.892673482 -0.543297127 -52.98983461 -1.698425925 31.61554051 25.73578923 82.38249347 33.86450601 -123.311882 Min.Variance: -41.8810356 -0.710108395 25.73578923 36.31192041 106.6853023 13.33648596 -142.9655466 -204.7759573 -1.700944652 82.38249347 106.6853023 521.1258721 -18.40125221 -497.0265612 Matice soustavy vps -52.77360681 -2.892673482 33.86450601 13.33648596 -18.40125221 113.0031104 -103.1339576 161 165.4 170.6 170.2 247.8 44 7 1 0 9.238318563 -0.543297127 -123.311882 -142.9655466 -497.0265612 -103.1339576 876.4459992 165.4 369.4 263 138.8 99 116 -19.8 1 0 170.6 263 748.4 769 733 207.6 687 1 0 170.2 138.8 769 1369.6 1198.2 103.2 1005.4 1 0 247.8 99 733 1198.2 1742.8 -42.4 1040.8 1 0 44 116 207.6 103.2 -42.4 179.4 148.8 1 0 7 -19.8 687 1005.4 1040.8 148.8 1149.2 1 0 1 1 1 1 1 1 1 0 1 InvM wi Rp VarP SigmaP 0.077541972 -0.006186729 0.008788437 -0.009709852 -0.037687458 -0.077748274 0.045001904 2.137199771 2.137199771 0.395249927 15.14374206 3.891496121 0.101567602 -0.006186729 0.007803096 -0.003616667 0.000167497 0.001056212 -0.000477668 0.001254258 0.04443472 0.04443472 0.008788437 -0.003616667 0.007543944 -0.002286279 -0.004259006 -0.008793788 0.00262336 -0.290668798 -0.290668798 -0.009709852 0.000167497 -0.002286279 0.004278044 0.004071768 0.010660407 -0.007181586 -0.230272848 -0.230272848 -0.037687458 0.001056212 -0.004259006 0.004071768 0.02058011 0.040174616 -0.023936242 -0.773325871 -0.773325871 -0.077748274 -0.000477668 -0.008793788 0.010660407 0.040174616 0.086382111 -0.050197403 -1.12240341 -1.12240341 0.045001904 0.001254258 0.00262336 -0.007181586 -0.023936242 -0.050197403 0.032435709 1.235036437 1.235036437 2.137199771 0.04443472 -0.290668798 -0.230272848 -0.773325871 -1.12240341 1.235036437 -30.28748412 lambda1 -30.28748412 zk 1 Pozadavek Rp=5% wi 0.393500391 0.437029695 -0.655179483 -0.044328174 0.036014728 0.415333712 0.417629131 Matice soustavy vps 12.46482586 14.22203112 -21.99148151 -1.484412384 1.755887217 3.595547509 0.575180292 161 165.4 170.6 170.2 247.8 44 7 1 1.9 0 14.22203112 35.27676809 -37.65277498 -1.344467347 0.779105534 10.52776359 -1.806911685 165.4 369.4 263 138.8 99 116 -19.8 1 6.1 0 -21.99148151 -37.65277498 160.6291498 11.16699892 -8.647974707 -28.24586151 -93.98917008 170.6 263 748.4 769 733 207.6 687 1 2.9 0 -1.484412384 -1.344467347 11.16699892 1.3456231 -0.956443464 -0.950006826 -9.306352769 170.2 138.8 769 1369.6 1198.2 103.2 1005.4 1 4 0 1.755887217 0.779105534 -8.647974707 -0.956443464 1.130258656 -0.317112373 7.827232162 247.8 99 733 1198.2 1742.8 -42.4 1040.8 1 5.7 0 3.595547509 10.52776359 -28.24586151 -0.950006826 -0.317112373 15.47343764 12.90508601 44 116 207.6 103.2 -42.4 179.4 148.8 1 3.4 0 0.575180292 -1.806911685 -93.98917008 -9.306352769 7.827232162 12.90508601 100.2183368 7 -19.8 687 1005.4 1040.8 148.8 1149.2 1 4.9 0 1 1 1 1 1 1 1 0 0 1 1.9 6.1 2.9 4 5.7 3.4 4.9 0 0 5 wi InvM 0.016039416 0.007660609 -0.004068331 -0.00315134 -0.009140957 -0.023510276 0.01617088 2.286870663 -0.378674055 1 0.393500391 Rp VarP SigmaP 0.007660609 0.00468536 -0.000721958 -0.001309155 -0.00537105 -0.012689387 0.007745581 0.010736227 0.085258694 2 0.437029695 5 39.86212538 6.313645966 0.791935441 -0.004068331 -0.000721958 0.004856308 -0.000915259 0.001708481 0.002544365 -0.003403606 -0.259380927 -0.079159711 3 -0.655179483 -0.00315134 -0.001309155 -0.000915259 0.003578658 0.001027626 0.004876574 -0.004107102 -0.246233458 0.040381057 4 -0.044328174 -0.009140957 -0.00537105 0.001708481 0.001027626 0.00733021 0.01499997 -0.01055428 -0.842795834 0.175762112 5 0.036014728 -0.023510276 -0.012689387 0.002544365 0.004876574 0.01499997 0.038550595 -0.024771841 -1.254395478 0.333945838 6 0.415333712 0.01617088 0.007745581 -0.003403606 -0.004107102 -0.01055428 -0.024771841 0.018920369 1.305198807 -0.177513935 7 0.417629131 2.286870663 0.010736227 -0.259380927 -0.246233458 -0.842795834 -1.254395478 1.305198807 -30.65171899 0.921530536 lambda1 -26.04406632 -0.378674055 0.085258694 -0.079159711 0.040381057 0.175762112 0.333945838 -0.177513935 0.921530536 -2.331513485 lambda2 -10.73603689 1 ##### Sheet/List 4 ##### Riziková portfolia A B C D 6.20% 4% 7.50% 8.40% 14.50% 9.70% 17% 20% rf 0.035 1. 2. 3. 4. 5. 0.2 0.4 0.5 0.6 0.8 Portfolio 0.8 0.6 0.5 0.4 0.2 Rp A 0.0566 0.0512 0.0485 0.0458 0.0404 B 0.039 0.038 0.0375 0.037 0.036 C 0.067 0.059 0.055 0.051 0.043 D 0.0742 0.0644 0.0595 0.0546 0.0448 ##### Sheet/List 5 ##### Rm 0.14 rf 0.06 Beta_i 1 1.235 2 0.268 3 1.997 4 2.45 ri 1 0.1588 2 0.08144 3 0.21976 4 0.256 ##### Sheet/List 6 ##### rf 7 ROK 1 10 9 22 0.666666667 5 defensivni agresivni 2 32 24 48 0.68 1.64 defensivni agresivni 3 20 14 30 0.538461538 1.769230769 defensivni agresivni 4 18 -2 -20 -0.818181818 -2.454545455 defensivni agresivni 5 17 16 29 0.9 2.2 defensivni agresivni 6 3 4 -3 0.75 2.5 defensivni agresivni 7 12 8 21 0.2 2.8 defensivni agresivni 8 -5 0 -15 0.583333333 1.833333333 defensivni agresivni 9 18 12 28 0.454545455 1.909090909 defensivni agresivni 10 21 15 36 0.571428571 2.071428571 defensivni agresivni E ® 14.6 10 17.6 "covar_m,i" 105.3777778 61.44444444 166.3777778 beta_i 1 0.583087305 1.578869675 i j E(ri) 11.43146352 18.99940953 rf i j Ri 7 11.43146352 18.99940953 beta_i 0 0.583087305 1.578869675